Curving mesh to other mesh
Lattice is useful if you have to deform a solid (like a 3D text on a curved surface). If it's only a plane to shrinkwrap to another curved plane, you can simply subdivide the mesh enough to get the desired resolution, adjust the view for the desired projection, go to edit mode, activate the face snapping and "project individual elements on the surface of other objects"; then select all vertices and slightly move the vertices: they will snap on the surface of any underlying object, with a view-dependent projection.